3D Simulation of Spindle Gravitational Collapse of a Collisionless Particle System

TL;DR

This study uses 3D numerical relativity simulations to investigate spindle gravitational collapse of a collisionless particle system, providing new insights into naked singularity formation and surpassing previous work by ST.

Contribution

The paper presents a novel 3D simulation approach that confirms naked singularity formation and extends beyond prior limitations of the ST study.

Findings

Peak curvature invariants reach maximum without horizon formation.

Results support naked singularity formation in axially symmetric collapse.

Simulation remains stable beyond previous code limitations.

Abstract

We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky(ST). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but go well beyond.We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.